2021/01/26 by Eduardo N. Marcos, Marcos, E., Octavio Mendoza +5 · 1 citation
Mathematics · #16D90 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 16G10 #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #Secondary 13E10
paper · pdf · doi:10.48550/arxiv.2101.10879
openalex publication_date 2021/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the lower triangular matrix \mathbbK-algebra Λ:=[\beginsmallmatrix T & 0 M & U \endsmallmatrix], where U and T are basic \mathbbK-algebras with enough idempotents and M is an U-T-bimodule where \mathbbK acts centrally. Moreover, we characterise in terms of U, T and M when, on one hand, the lower triangular matrix \mathbbK-algebra Λ is standardly stratified in the sense of the paper "A generalization theory of standardly stratified algebras I: Standardly stratified ringois"; and on another hand, when Λ is locally bounded in the sense of the paper "Locally finite generated modules over rings with enough idempotents". Finally, it is also studied several properties relating the projective dimensions in the categories of finitely generated modules mod(U), mod(T) and mod(Λ).